Billy's was a one room enterprise with the cooks on display and a counter that formed a U around them. We sat on stools and watched our burgers get grilled, fries get deep fried, sodas get drawn, etc. The cooks were rude in a good-humored way, wore funny hats, dreamed up outrageous "house rules," and made themselves useful by handing us our meals straight from the grill and deep fryer.
The pre-cooking prep was done in The Cadillac's kitchen and you could also order a Billy burger in their bar. The DrsC have fond memories of Billy's on the Square. Examples include meeting VP Dick Cheney's Secret Service detail at Billy's, taking a meal break. Cheney's WY place is in nearby Wilson.
We spotted the curly cords running from the earpieces down under their collars and asked. They were whining about having to run a couple more miles to burn off the calories.
Another time we met someone we had seen on TV, sitting alongside us munching a burger. Mario Gabelli, a big-deal investor and wealthy market analyst. He is a distinctive-looking gentleman who had been a frequent guest on Louis Rukeyser's Wall Street Week program on PBS. He had a place in Jackson and would hold seminars there for his largest investors.
Another time we'd finished our meal and were walking to our vehicle when we passed Harrison Ford on the boardwalk outside the Million Dollar Bar, carrying a six pack of bottled beer. Wikipedia says he's 6'1" but he sure looked shorter than that to me. Maybe he didn't have his heels on. He lives near here.
Anyway, The Cadillac folded and, with it, Billy's. A year or so later the owners got a new restaurant named "The Lift" on south Cache by the Snow King ski lift. We went there for burgers for several years. Then that restaurant closed, and the building was razed to put up condos. The mountains hemming in Jackson make developable land scarce and therefore super valuable.
Now Billy's has been revived again, this time co-located with The Virginian hotel-restaurant-saloon combination on west Broadway. We'll have to give it a try, Billy's is a part of old Jackson lore.